Chapter 2, Problem 49RE

Position Velocity and Acceleration A car traveling on a straight road and $s\left(t\right)$ is the distance travelled after $t$ hours. Match each set of information about $s\left(t\right)$ and its derivative with the corresponding description of the car’s motion.

Information:

A. $s\left(t\right)$ is a constant function.

B. $s\text{'}\left(t\right)$ is a positive constant function.

C. $s\text{'}\left(t\right)$ is positive at $t=a$.

D. $s\text{'}\left(t\right)$ is negative at $t=a$.

E. $s\text{'}\left(t\right)$ and $s\text{'}\text{'}\left(t\right)$ are positive at $t=a$.

F. $s\text{'}\left(t\right)$ is positive and $s\text{'}\text{'}\left(t\right)$ is negative at $t=a$.

Descriptions:

$a$. The car is moving forward and speeding up at time $a$.

$b$. The car is backing up at time $a$.

$c$. The car is standing still.

$d$. The car is moving forward, but slowing down at time $a$.

e. The car is moving forward at a steady rate.

f. The car is moving forward at time $a$.